Cmes-computer Modeling in Engineering & Sciences, 2004
This work is concerned with the computation of the contribution of initial conditions in twodimen... more This work is concerned with the computation of the contribution of initial conditions in twodimensional (2D) frequency-domain analysis of transient scalar wave propagation problems with the corresponding Boundary Element Method (BEM) formulation. The paper describes how pseudo-forces, represented by generalized functions, can replace the initial conditions, related to the potential and its time derivative. The generation of such pseudo-forces is the subject of a detailed discussion. The formulation presented here carries out Discrete Fourier Transform (Direct: DFT, and Inverse: IDFT) via FFT (Fast Fourier Transform) algorithms. At the end of the paper four examples are presented in order to show the potentialities and accuracy of the approach. keyword: Boundary elements, Helmholtz equation, frequency domain, scalar wave equation, Fourier transform, initial conditions.
O trabalho tem como objetivo apresentar resultados preliminares referentes ao projeto que visa de... more O trabalho tem como objetivo apresentar resultados preliminares referentes ao projeto que visa desenvolver uma ferramenta computacional capaz de otimizar estruturas de concreto armado modeladas como pórticos espaciais, tendo como restrições os procedimentos da norma brasileira “ABNT (2014) NBR 6118: Projeto de Estruturas de Concreto”. Tal projeto consiste na implementação de um método de otimização inspirado na natureza chamado de algoritmo genético, o qual constitui-se de uma rotina de análise de estruturas baseada no Método dos Deslocamentos, e de uma sub-rotina de dimensionamento capaz de calcular a quantidade de aço necessária e verificar todas as restrições, segundo a NBR 6118. Até o momento, o algoritmo genético foi implementado e testado para minimização de funções de várias variáveis. Serão apresentados resultados referentes ao estudo do comportamento do algoritmo em função do número de variáveis de otimização, e parâmetros como número total de avaliações da função objetivo ...
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2021
This work presents a boundary element method formulation for the solution of the diffusion–advect... more This work presents a boundary element method formulation for the solution of the diffusion–advection problem. The formulation, developed for two-dimensional problems, for non-isotropic media, considers a spatially variable velocity field. The only way to deal with such a kind of problem is employing a steady-state fundamental solution. Consequently, the basic BEM equation presents one domain integral related to the velocity components, and another one related to the time derivative of the variable of interest, which is approximated using a backward finite difference scheme. BEM results are compared with an available analytical solution in the first part of the first example, and with the results provided by a finite element method formulation, taken as reference ones, in the second part of the first example and in the second example. From the comparisons, one can observe a good agreement between the results furnished by the proposed formulation and the analytical and reference solutions.
Pesquisa e Ensino em Ciências Exatas e da Natureza, 2018
No projeto de edificações, os projetistas buscam soluções otimizadas e seguras relativas a divers... more No projeto de edificações, os projetistas buscam soluções otimizadas e seguras relativas a diversos aspectos estruturais, além da redução dos custos de material e mão-de-obra. Os métodos de otimização podem ser empregados nesse objetivo sem comprometer a segurança estrutural. Dessa forma, este artigo tem por objetivo a otimização estrutural por Algoritmos Genéticos de um pórtico espacial de concreto armado. Para o estudo foi desenvolvido um programa de Algoritmos Genéticos, contemplando o dimensionamento das armaduras dos elementos estruturais. A função objetivo é formada pelos custos de concreto, forma e aço e será minimizada, sujeita a restrições da NBR 6118:2014 (Projeto de Estruturas de Concreto - Procedimento). O modelo estrutural é processado no programa Ansys ®, onde a discretização se dá via método dos elementos finitos, para a análise e obtenção dos esforços e deformações na estrutura. Neste estudo são consideradas variáveis de projeto: altura da seção transversal das vigas...
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2016
Pollution error is a well known source of inaccuracies in continuous or discontinuous FE approach... more Pollution error is a well known source of inaccuracies in continuous or discontinuous FE approaches to solve the Helmholtz equation. This topic is widely studied in a large number of papers, e.g., (Ihlenburg and Babuška, Comput Math Appl 30(9):9–37, 1995; Ihlenburg, Finite element analysis of acoustic scattering applied mathematical sciences, vol 132. Springer, New York, 1998). Robust methodologies for structured square meshes have been developed in recent years. This work seeks to develop a methodology based on Petrov–Galerkin discontinuous formulation, to minimize phase error for Helmholtz equation for both structured and unstructured meshes. A Petrov–Galerkin finite element formulation is introduced for the Helmholtz problem in two dimensions using polynomial weighting functions. At each node of the triangular mesh, a global basis function for the weighting space is obtained, adding bilinear $$C^0$$C0 Lagrangian weighting function linear combinations. The optimal weighting functions, with the same support of the corresponding global test functions, are obtained after computing the coefficients of these linear combinations attending to optimal criteria. This is done numerically through a preprocessing technique that is naturally applied to non-uniform and unstructured meshes. In particular, for uniform meshes a quasi optimal interior stencil of the same order of the quasi-stabilized finite element method stencil derived by (Babuška et al., Comput Meth Appl Mech Eng 128:325–359, 1995) is obtained. The numerical results indicate a better performance in relation to the classic discontinuous Galerkin method.
ABSTRACT This work presents a strategy to initialize numerical methods applied to solve time-depe... more ABSTRACT This work presents a strategy to initialize numerical methods applied to solve time-dependent wave propagation problems, e.g., transient acoustics. The strategy described here is dedicated to model wave propagating from air guns in offshore geophysical surveys applied to oil and gas industry. The model is formed by two distinct regions, i.e., a homogeneous (water) and a heterogeneous (sediment) one. For the geophysical applications considered here, the integrals of the BEM formulation can be simplified so that the final expressions allow one to calculate the wavefield in the homogeneous region, at any time, without needing to march on time through a time-stepping algorithm. Thus, this wavefield can be used to initialize any numerical method employed to propagate the pressure field throughout the model; in this work, the finite difference method (FDM) is the numerical method considered. The final integral equations for two- and three-dimensional problems are presented. An assessment of the accuracy of the results obtained by the strategy proposed here is provided at the end of this work, through the analysis of three examples.
SEG Technical Program Expanded Abstracts 2015, 2015
Because the grid spacing is fixed in the finite-difference method (FDM), the numerical dispersion... more Because the grid spacing is fixed in the finite-difference method (FDM), the numerical dispersion usually imposes the use of restrictive small grid spacing (given by the lower velocity) in the whole model. Then, the number of grid points per wave-length is too large in deep layers, resulting in loss of efficiency of the FDM. Although the use of high-order operators allows bigger grid spacing and could make FDM more efficient, this does not solve the problem. In this paper, we develop a new 3D explicit scheme based on finite-volume method (FVM) that addresses the aforementioned problem in an efficient way. The algorithm is constructed using a general formalism with sparse matrices and allows both the use of different grid spacing in layers with different velocities and the refinement in regions of interest using OcTree meshes. OcTree is easy to generate using regular grids, avoiding additional complications in meshing. Computational tools for parallel processing on the GPU were used for the algebraic manipulation of the sparse matrices. The numerical scheme can be seen as an extension of the staggered-grid scheme; actually, it reduces to the classical staggered-grid scheme for the case of regular grids. Finally, an example is presented to show the effectiveness of the method.
SEG Technical Program Expanded Abstracts 2010, 2010
In the universe of tomographic techniques aiming to determine the subsurface velocity field, inve... more In the universe of tomographic techniques aiming to determine the subsurface velocity field, inversion over CFP Operators (CFPOs) reduces depth-velocity ambiguity. Its main drawback is the operator estimation for very complex areas, where conventional CFPO estimation is damaged by the non-continuity of events and diffractions. We overcome this problem using diffractions in Common Offset Gathers (COG) to estimate CFPOs. A synthetic example based on a geologic-geophysics model of the Santos Basin (offshore Brazil) is used to validate the idea. An overview of the inversion workflow is presented in which a Singular Value Decomposition (SVD) pseudo-inverse technique is explored.
Cmes-computer Modeling in Engineering & Sciences, 2004
This work is concerned with the computation of the contribution of initial conditions in twodimen... more This work is concerned with the computation of the contribution of initial conditions in twodimensional (2D) frequency-domain analysis of transient scalar wave propagation problems with the corresponding Boundary Element Method (BEM) formulation. The paper describes how pseudo-forces, represented by generalized functions, can replace the initial conditions, related to the potential and its time derivative. The generation of such pseudo-forces is the subject of a detailed discussion. The formulation presented here carries out Discrete Fourier Transform (Direct: DFT, and Inverse: IDFT) via FFT (Fast Fourier Transform) algorithms. At the end of the paper four examples are presented in order to show the potentialities and accuracy of the approach. keyword: Boundary elements, Helmholtz equation, frequency domain, scalar wave equation, Fourier transform, initial conditions.
O trabalho tem como objetivo apresentar resultados preliminares referentes ao projeto que visa de... more O trabalho tem como objetivo apresentar resultados preliminares referentes ao projeto que visa desenvolver uma ferramenta computacional capaz de otimizar estruturas de concreto armado modeladas como pórticos espaciais, tendo como restrições os procedimentos da norma brasileira “ABNT (2014) NBR 6118: Projeto de Estruturas de Concreto”. Tal projeto consiste na implementação de um método de otimização inspirado na natureza chamado de algoritmo genético, o qual constitui-se de uma rotina de análise de estruturas baseada no Método dos Deslocamentos, e de uma sub-rotina de dimensionamento capaz de calcular a quantidade de aço necessária e verificar todas as restrições, segundo a NBR 6118. Até o momento, o algoritmo genético foi implementado e testado para minimização de funções de várias variáveis. Serão apresentados resultados referentes ao estudo do comportamento do algoritmo em função do número de variáveis de otimização, e parâmetros como número total de avaliações da função objetivo ...
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2021
This work presents a boundary element method formulation for the solution of the diffusion–advect... more This work presents a boundary element method formulation for the solution of the diffusion–advection problem. The formulation, developed for two-dimensional problems, for non-isotropic media, considers a spatially variable velocity field. The only way to deal with such a kind of problem is employing a steady-state fundamental solution. Consequently, the basic BEM equation presents one domain integral related to the velocity components, and another one related to the time derivative of the variable of interest, which is approximated using a backward finite difference scheme. BEM results are compared with an available analytical solution in the first part of the first example, and with the results provided by a finite element method formulation, taken as reference ones, in the second part of the first example and in the second example. From the comparisons, one can observe a good agreement between the results furnished by the proposed formulation and the analytical and reference solutions.
Pesquisa e Ensino em Ciências Exatas e da Natureza, 2018
No projeto de edificações, os projetistas buscam soluções otimizadas e seguras relativas a divers... more No projeto de edificações, os projetistas buscam soluções otimizadas e seguras relativas a diversos aspectos estruturais, além da redução dos custos de material e mão-de-obra. Os métodos de otimização podem ser empregados nesse objetivo sem comprometer a segurança estrutural. Dessa forma, este artigo tem por objetivo a otimização estrutural por Algoritmos Genéticos de um pórtico espacial de concreto armado. Para o estudo foi desenvolvido um programa de Algoritmos Genéticos, contemplando o dimensionamento das armaduras dos elementos estruturais. A função objetivo é formada pelos custos de concreto, forma e aço e será minimizada, sujeita a restrições da NBR 6118:2014 (Projeto de Estruturas de Concreto - Procedimento). O modelo estrutural é processado no programa Ansys ®, onde a discretização se dá via método dos elementos finitos, para a análise e obtenção dos esforços e deformações na estrutura. Neste estudo são consideradas variáveis de projeto: altura da seção transversal das vigas...
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2016
Pollution error is a well known source of inaccuracies in continuous or discontinuous FE approach... more Pollution error is a well known source of inaccuracies in continuous or discontinuous FE approaches to solve the Helmholtz equation. This topic is widely studied in a large number of papers, e.g., (Ihlenburg and Babuška, Comput Math Appl 30(9):9–37, 1995; Ihlenburg, Finite element analysis of acoustic scattering applied mathematical sciences, vol 132. Springer, New York, 1998). Robust methodologies for structured square meshes have been developed in recent years. This work seeks to develop a methodology based on Petrov–Galerkin discontinuous formulation, to minimize phase error for Helmholtz equation for both structured and unstructured meshes. A Petrov–Galerkin finite element formulation is introduced for the Helmholtz problem in two dimensions using polynomial weighting functions. At each node of the triangular mesh, a global basis function for the weighting space is obtained, adding bilinear $$C^0$$C0 Lagrangian weighting function linear combinations. The optimal weighting functions, with the same support of the corresponding global test functions, are obtained after computing the coefficients of these linear combinations attending to optimal criteria. This is done numerically through a preprocessing technique that is naturally applied to non-uniform and unstructured meshes. In particular, for uniform meshes a quasi optimal interior stencil of the same order of the quasi-stabilized finite element method stencil derived by (Babuška et al., Comput Meth Appl Mech Eng 128:325–359, 1995) is obtained. The numerical results indicate a better performance in relation to the classic discontinuous Galerkin method.
ABSTRACT This work presents a strategy to initialize numerical methods applied to solve time-depe... more ABSTRACT This work presents a strategy to initialize numerical methods applied to solve time-dependent wave propagation problems, e.g., transient acoustics. The strategy described here is dedicated to model wave propagating from air guns in offshore geophysical surveys applied to oil and gas industry. The model is formed by two distinct regions, i.e., a homogeneous (water) and a heterogeneous (sediment) one. For the geophysical applications considered here, the integrals of the BEM formulation can be simplified so that the final expressions allow one to calculate the wavefield in the homogeneous region, at any time, without needing to march on time through a time-stepping algorithm. Thus, this wavefield can be used to initialize any numerical method employed to propagate the pressure field throughout the model; in this work, the finite difference method (FDM) is the numerical method considered. The final integral equations for two- and three-dimensional problems are presented. An assessment of the accuracy of the results obtained by the strategy proposed here is provided at the end of this work, through the analysis of three examples.
SEG Technical Program Expanded Abstracts 2015, 2015
Because the grid spacing is fixed in the finite-difference method (FDM), the numerical dispersion... more Because the grid spacing is fixed in the finite-difference method (FDM), the numerical dispersion usually imposes the use of restrictive small grid spacing (given by the lower velocity) in the whole model. Then, the number of grid points per wave-length is too large in deep layers, resulting in loss of efficiency of the FDM. Although the use of high-order operators allows bigger grid spacing and could make FDM more efficient, this does not solve the problem. In this paper, we develop a new 3D explicit scheme based on finite-volume method (FVM) that addresses the aforementioned problem in an efficient way. The algorithm is constructed using a general formalism with sparse matrices and allows both the use of different grid spacing in layers with different velocities and the refinement in regions of interest using OcTree meshes. OcTree is easy to generate using regular grids, avoiding additional complications in meshing. Computational tools for parallel processing on the GPU were used for the algebraic manipulation of the sparse matrices. The numerical scheme can be seen as an extension of the staggered-grid scheme; actually, it reduces to the classical staggered-grid scheme for the case of regular grids. Finally, an example is presented to show the effectiveness of the method.
SEG Technical Program Expanded Abstracts 2010, 2010
In the universe of tomographic techniques aiming to determine the subsurface velocity field, inve... more In the universe of tomographic techniques aiming to determine the subsurface velocity field, inversion over CFP Operators (CFPOs) reduces depth-velocity ambiguity. Its main drawback is the operator estimation for very complex areas, where conventional CFPO estimation is damaged by the non-continuity of events and diffractions. We overcome this problem using diffractions in Common Offset Gathers (COG) to estimate CFPOs. A synthetic example based on a geologic-geophysics model of the Santos Basin (offshore Brazil) is used to validate the idea. An overview of the inversion workflow is presented in which a Singular Value Decomposition (SVD) pseudo-inverse technique is explored.
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